(Updates with closing prices) TOKYO, Oct 27 (Reuters) - Japan's Nikkei share average rebounded on Tuesday after optimism returned to the AI sector following a filing by industry bellwether Anthropic to list its shares. The benchmark Nikkei 225 advanced 1.73% to close at 63,268.37, paring an earlier gain of more than 2%. The broader Topix rose 0.61% to 3,997.37. Anthropic disclosed steep losses and red-hot revenue growth in its filing for a US initial public offering, laying out its ambition to build AI systems capable of reshaping the global economy despite the high costs of developing the technology.